Primitive of x by Power of a x + b/Also presented as

Primitive of $x$ by Power of $a x + b$: Also presented as

This result is also seen presented in the form:

$\ds \int x \paren {a x + b}^n \rd x = \frac {\paren {a x + b}^{n + 1} } {a^2} \paren {\frac {a x + b} {n + 2} - \frac b {n + 1} } + C$

where $n \ne - 1$ and $n \ne - 2$.

Also see

• Primitive of $x$ over $a x + b$ for the case when $n = -1$
• Primitive of $x$ over $\paren {a x + b}^2$ for the case when $n = -2$

Sources

• 1968: George B. Thomas, Jr.: Calculus and Analytic Geometry (4th ed.) ... (previous) ... (next): Front endpapers: A Brief Table of Integrals: $7$.